Likelihood-based inference for multivariate skew scale mixtures of normal distributions

Scale mixtures of normal distributions are often used as a challenging class for statistical analysis of symmetrical data. Recently, Ferreira et al. (Stat Methodol 8:154–171, 2011 ) defined the univariate skew scale mixtures of normal distributions that offer much needed flexibility by combining both skewness with heavy tails. In this paper, we develop a multivariate version of the skew scale mixtures of normal distributions, with emphasis on the multivariate skew-Student- t , skew-slash and skew-contaminated normal distributions. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine expectation/conditional maximisation either algorithms for maximum likelihood estimation. The observed information matrix is derived analytically to account for standard errors. Results obtained from real and simulated datasets are reported to illustrate the usefulness of the proposed method.